Abstract:

There are two stable isotopes of helium: helium-3 and helium-4. Both exhibit superfluidity at low temperatures, helium-3 at around 1 mK. The superfluidity brings some special features to the fluid, such as the possibility of frictionless mass flow and quantization of flow through vortex lines. This thesis consists of experiments performed on superfluid helium-3 under rotation, and on the vortex lines the rotation induces. The cylindrical sample is probed using nuclear magnetic resonance (NMR) and there is a possibility to stabilize two superfluid phases, the A phase and the B phase, simultaneously in the sample. We study two aspects: the dynamics of the phase boundary between the A and the B phases, and turbulent vortex dynamics in the B phase.

When a sample which consists of both the A and the B phases is rotated, a velocity difference in the superfluid components can form across the phase boundary. At a sufficiently high velocity the boundary becomes unstable towards wave formation, analogously to the Kelvin-Helmholtz instability in classical hydrodynamics (e.g. waves form on water while wind blows over the surface). In regular fluids their viscosity affects the instability, these experiments are the first demonstration of the instability in superfluids. We present measurements on the criterion for the instability, and how vortex lines cross the phase boundary as a result. The instability turned out to provide unprecedented flexibility in vortex injection into the B phase and is used in the study of turbulent vortex dynamics.

Many questions remain unanswered regarding classical turbulence. In a superfluid, turbulence is seen as a chaotic motion of vortex lines. Turbulence has been studied intensively in superfluid helium-4, the measurements in this thesis are one of the first to show turbulent flow in the B phase of helium-3. Experiments in helium-3 give new insight into turbulent vortex dynamics since the two fluids differ in their hydrodynamic properties, for example, in terms of damping of vortex motion, vortex formation, and the dynamics of the normal fluid background. We study which effects are important in the formation of a turbulent vortex network, how the vortex lines spread into the vortex free region, and finally how they relax into the equilibrium state. We identify a similarity parameter for the flow in an analogous fashion to the Reynolds number in normal fluid dynamics. Unlike in regular fluids, the hydrodynamic transition between regular and turbulent vortex dynamics appears to be controlled by intrinsic parameters only.